AR1 analyses of Peters data

Parameter priors

AR1 model analyses:

	NuPrimeMu	NuPrimeSa	KappaMu	KappaSa	OmegaMu	OmegaSa	mMu	mSa	PhiMu	PhiSa	Sig2Mu	Sig2Sa
A25	128	1	NaN, -Inf	NaN, 0	NaN, -2, 0	NaN, 16, 0	NaN, 1, 1	NaN, 0.5, 0	NaN, -2.2, -Inf	NaN, 2, 0	0, 4	0, 0
A26	128	1	NaN, -Inf	NaN, 0	NaN, -2, 0	NaN, 16, 0	NaN, 1, 1	NaN, 0.25, 0	NaN, -2.2, -Inf	NaN, 2, 0	0, 4	0, 0
A27	128	1	NaN, -Inf	NaN, 0	NaN, -2, 0	NaN, 16, 0	NaN, 0, 1	NaN, 1, 0	NaN, -2.2, -Inf	NaN, 2, 0	0, 4	0, 0
A28	128	1	NaN, 0	NaN, 0	NaN, -2, -6	NaN, 16, 16	NaN, 0, 1	NaN, 1, 0	NaN, -2.2, -Inf	NaN, 2, 0	0, 4	0, 0
A29	128	1	NaN, 0	NaN, 0	NaN, -2, -6	NaN, 16, 16	NaN, 0, 1	NaN, 1, 1	NaN, -2.2, -2.2	NaN, 2, 2	0, 4	0, 0
A31	128	1	NaN, -Inf	NaN, 0	NaN, -2, 0	NaN, 16, 0	NaN, -Inf, -Inf	NaN, 0, 0	NaN, -2.2, -Inf	NaN, 2, 0	0, 4	0, 0
A32	128	1	NaN, -Inf	NaN, 0	NaN, -2, 0	NaN, 16, 0	NaN, -Inf, -Inf	NaN, 0, 0	NaN, -Inf, -Inf	NaN, 0, 0	0, 4	1, 0
A33	128	1	NaN, -Inf	NaN, 0	NaN, -2, 0	NaN, 16, 0	NaN, -Inf, -Inf	NaN, 0, 0	NaN, -2.2, -Inf	NaN, 2, 0	0, 4	1, 0

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Test of ANOVA assumptions

Shapiro-Wilk tests of normality of residuals

[<0.05 = NOT normal]

	Model_names	SW_omega2	SW_omega3	SW_nu	SW_M2	SW_M3	SW_phi2	SW_phi3
1	A25	0.0932		0.00666	0.00038	1.21e-19	0.00022
2	A26	0.269		0.0108	0.646	1.21e-19	0.000787
3	A27	0.0112		0.00527	0.0432	1.21e-19	3.08e-05
4	A28	0.0687	6.8e-15	0.00356	0.0324	1.21e-19	3.36e-06
5	A29	0.0225	3.78e-13	0.00505	0.039	3.81e-13	2.87e-05	4.24e-15
6	A31	0.000953		0.00506			1.64e-10
7	A32	2.08e-05		0.00158
8	A33	0.000956		0.00507			1.64e-10

Test for homoskedasticity (homogeneity of variance)

Brown-Forsyth test (uses the median - more robust to outliers)

[<0.05 = VIOLATION of homogeneity of variance]

	Model_names	BF_omega2	BF_omega3	BF_nu	BF_M2	BF_M3	BF_phi2	BF_phi3
1	A25	0.000877		0.195	0.926		0.00547
2	A26	0.00722		0.158	0.685		0.00856
3	A27	0.00674		0.0876	0.329		0.00176
4	A28	0.00572	0.0621	0.107	0.49		0.00445
5	A29	0.00304	0.0319	0.0763	0.437	0.0585	0.00338	0.0814
6	A31	0.488		0.908			0.0108
7	A32	0.515		0.706
8	A33	0.489		0.908			0.0108

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Fit - beads of opposite colour (BOOC) for selected analyses

	Analysis_no.	Fit_BOOC
1	A25	0.0082
2	A26	0.0087
3	A27	0.00801
4	A28	0.0081
5	A29	0.00731
6	A31	0.0219
7	A32	0.0213
8	A33	0.0219

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Means, SDs, ANOVA summaries and post-hoc tests

Mean/SD table

	Om2			Om3			log(Nu)			M2			M3			Phi2			Phi3
	Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD
A25
Ctrl	-3.44	1.42		0	0		3.86	1.02		1.71	1.21		1	0		0.23	0.204		0	0
Pat	-1.7	2.51		0	0		3.6	1.36		1.37	0.945		1	0		0.432	0.282		0	0
Psych ctrl	-2.22	2.7		0	0		3.3	1.4		1.16	0.991		1	0		0.36	0.302		0	0
A26
Ctrl	-3.66	1.57		0	0		3.72	1.06		1.71	0.692		1	0		0.23	0.187		0	0
Pat	-1.72	2.49		0	0		3.55	1.36		1.36	0.798		1	0		0.442	0.291		0	0
Psych ctrl	-2.74	2.64		0	0		3.21	1.44		1.28	0.709		1	0		0.305	0.294		0	0
A27
Ctrl	-3.28	1.48		0	0		4.01	0.966		3.24	1.92		2.72	0		0.147	0.177		0	0
Pat	-1.66	2.41		0	0		3.62	1.34		1.79	1.46		2.72	0		0.422	0.311		0	0
Psych ctrl	-2.51	2.63		0	0		3.32	1.43		1.96	1.88		2.72	0		0.253	0.284		0	0
A28
Ctrl	-4.24	1.49		-6	0.0143		4	0.974		3.18	1.85		2.72	0		0.139	0.164		0	0
Pat	-2.43	2.44		-6.01	0.0326		3.56	1.32		1.81	1.47		2.72	0		0.38	0.298		0	0
Psych ctrl	-3.14	3		-5.98	0.0831		3.38	1.43		1.9	1.87		2.72	0		0.285	0.3		0	0
A29
Ctrl	-4.52	1.37		-6	0.00598		4.01	0.958		3.2	1.89		2.04	0.591		0.157	0.191		0.0884	0.0394
Pat	-2.66	2.58		-5.98	0.0413		3.61	1.34		1.81	1.54		2.11	0.605		0.419	0.307		0.135	0.131
Psych ctrl	-3.19	2.84		-5.99	0.0467		3.4	1.41		2.03	1.93		2.58	2.13		0.271	0.273		0.0819	0.0224
A31
Ctrl	-1.25	1.44		0	0		2.6	1.2		0	0		0	0		0.0696	0.123		0	0
Pat	-0.081	1.4		0	0		2.45	1.22		0	0		0	0		0.163	0.217		0	0
Psych ctrl	-0.666	1.85		0	0		2.6	1.17		0	0		0	0		0.225	0.255		0	0
A32
Ctrl	-1.38	1.55		0	0		2.66	1.21		0	0		0	0		0	0		0	0
Pat	-0.46	1.13		0	0		2.28	0.992		0	0		0	0		0	0		0	0
Psych ctrl	-1.45	1.57		0	0		2.4	1.07		0	0		0	0		0	0		0	0
A33
Ctrl	-1.25	1.44		0	0		2.6	1.2		0	0		0	0		0.0695	0.123		0	0
Pat	-0.0811	1.4		0	0		2.45	1.22		0	0		0	0		0.163	0.217		0	0
Psych ctrl	-0.666	1.85		0	0		2.6	1.17		0	0		0	0		0.225	0.255		0	0

ANOVA model summaries table

	Om2			Om3			log(Nu)			M2			M3			Phi2			Phi3
	F(2,80)	p		F(2,80)	p		F(2,80)	p		F(2,80)	p		F(2,80)	p		F(2,80)	p		F(2,80)	p
A25	5.2	0.0075					1.5	0.24		1.9	0.16		0.65	0.53		4.9	0.01
A26	5.8	0.0043					1.1	0.33		2.9	0.059		0.65	0.53		5.2	0.0073
A27	4.3	0.017					2.3	0.11		6	0.0036		0.65	0.53		8.8	0.00036
A28	4.9	0.0095		1.8	0.17		2	0.14		5.9	0.004		0.65	0.53		7.2	0.0014
A29	5.7	0.0049		1.4	0.26		1.9	0.16		5.3	0.0071		1.5	0.23		8	7e-04		3.6	0.032
A31	4.2	0.018					0.13	0.88								4.7	0.012
A32	3.8	0.027					0.91	0.41
A33	4.2	0.018					0.13	0.88								4.7	0.012

Tukey HSD post-hoc tests

	Om2		Om3		log(Nu)		M2		M3		Phi2		Phi3
	p.adj		p.adj		p.adj		p.adj		p.adj		p.adj		p.adj
A25
Pat-Ctrl	0.0077				0.69		0.45		1		0.0092
Psych ctrl-Ctrl	0.1				0.21		0.15		1		0.15
Psych ctrl-Pat	0.68				0.68		0.78		1		0.61
A26
Pat-Ctrl	0.0029				0.86		0.17		1		0.005
Psych ctrl-Ctrl	0.27				0.3		0.081		1		0.52
Psych ctrl-Pat	0.25				0.63		0.92		1		0.16
A27
Pat-Ctrl	0.013				0.44		0.0071		0.61		0.00021
Psych ctrl-Ctrl	0.38				0.098		0.027		0.63		0.27
Psych ctrl-Pat	0.37				0.68		0.94		1		0.062
A28
Pat-Ctrl	0.0079		0.79		0.36		0.0094		0.61		0.0011
Psych ctrl-Ctrl	0.18		0.36		0.15		0.022		0.63		0.085
Psych ctrl-Pat	0.52		0.16		0.86		0.98		1		0.4
A29
Pat-Ctrl	0.0053		0.25		0.42		0.011		0.98		0.00043		0.058
Psych ctrl-Ctrl	0.077		0.54		0.16		0.049		0.23		0.22		0.95
Psych ctrl-Pat	0.69		0.9		0.82		0.91		0.37		0.12		0.054
A31
Pat-Ctrl	0.013				0.89						0.16
Psych ctrl-Ctrl	0.35				1						0.011
Psych ctrl-Pat	0.4				0.9						0.52
A32
Pat-Ctrl	0.042				0.4
Psych ctrl-Ctrl	0.99				0.67
Psych ctrl-Pat	0.056				0.93
A33
Pat-Ctrl	0.013				0.89						0.16
Psych ctrl-Ctrl	0.35				1						0.011
Psych ctrl-Pat	0.4				0.9						0.52

Parametric effect sizes (eta-squared)

	Om2		Om3		log(Nu)		M2		M3		Phi2		Phi3
A25	0.12				0.035		0.046		Inf		0.11
A26	0.13				0.027		0.068		Inf		0.12
A27	0.097				0.054		0.13		Inf		0.18
A28	0.11		0.043		0.048		0.13		Inf		0.15
A29	0.12		0.033		0.045		0.12		0.036		0.17		0.083
A31	0.096				0.0033						0.1
A32	0.086				0.022
A33	0.096				0.0033						0.1

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Non-parametric tests (Kruskal-Wallis)

	Om2			Om3			log(Nu)			M2			M3			Phi2			Phi3
	Chi sq(2, n=83)	p		Chi sq(2, n=83)	p		Chi sq(2, n=83)	p		Chi sq(2, n=83)	p		Chi sq(2, n=83)	p		Chi sq(2, n=83)	p		Chi sq(2, n=83)	p
A25	6.84	0.033					2.55	0.28		6.19	0.045					5.68	0.058
A26	7.76	0.021					2.08	0.35		4.81	0.09					6.59	0.037
A27	4.8	0.091					3.11	0.21		8.75	0.013					17.3	0.00018
A28	7.23	0.027		0.224	0.89		3.59	0.17		9.16	0.01					15.1	0.00053
A29	6.25	0.044		0.181	0.91		2.93	0.23		8.12	0.017		0.301	0.86		15.9	0.00035		2.58	0.28
A31	8.42	0.015					0.28	0.87								14.2	0.00083
A32	8.52	0.014					1.09	0.58
A33	8.42	0.015					0.28	0.87								14	0.00091

Post-hoc non-parametric tests (Dunn test)

	Om2		Om3		log(Nu)		M2		M3		Phi2		Phi3
A25
Pat-Ctrl	0.016				0.28		0.11				0.026
Psych ctrl-Ctrl	0.12				0.17		0.026				0.19
Psych ctrl-Pat	0.2				0.34		0.22				0.19
A26
Pat-Ctrl	0.0082				0.32		0.12				0.021
Psych ctrl-Ctrl	0.1				0.23		0.065				0.39
Psych ctrl-Pat	0.19				0.36		0.32				0.054
A27
Pat-Ctrl	0.044				0.29		0.018				5.3e-05
Psych ctrl-Ctrl	0.27				0.13		0.016				0.11
Psych ctrl-Pat	0.17				0.26		0.5				0.01
A28
Pat-Ctrl	0.011		0.43		0.21		0.013				0.00015
Psych ctrl-Ctrl	0.21		0.73		0.11		0.016				0.043
Psych ctrl-Pat	0.11		0.96		0.29		0.44				0.061
A29
Pat-Ctrl	0.024		1		0.26		0.02		0.88		9.9e-05		0.25
Psych ctrl-Ctrl	0.12		0.78		0.15		0.023		0.79		0.047		0.28
Psych ctrl-Pat	0.24		0.46		0.31		0.47		0.41		0.045		0.18
A31
Pat-Ctrl	0.0056				0.69						0.00089
Psych ctrl-Ctrl	0.15				0.44						0.0057
Psych ctrl-Pat	0.11				0.92						0.31
A32
Pat-Ctrl	0.019				0.47
Psych ctrl-Ctrl	0.25				0.53
Psych ctrl-Pat	0.01				0.37
A33
Pat-Ctrl	0.0056				0.69						0.00092
Psych ctrl-Ctrl	0.15				0.44						0.0061
Psych ctrl-Pat	0.11				0.92						0.3

Non-parametric effect sizes

(Eta-squared = Kruskal-Wallis Chi-sq statistic / N-1)

	Om2		Om3		log(Nu)		M2		M3		Phi2		Phi3
A25	0.0834				0.0311		0.0755				0.0693
A26	0.0946				0.0254		0.0587				0.0804
A27	0.0585				0.0379		0.107				0.211
A28	0.0882		0.00273		0.0438		0.112				0.184
A29	0.0762		0.00221		0.0357		0.099		0.00367		0.194		0.0315
A31	0.103				0.00341						0.173
A32	0.104				0.0133
A33	0.103				0.00341						0.171

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Plots

Box & density plots of parameter posteriors